The goal of this research is to discover the cortical computations that determine the response properties of neurons in visual cortical areas V2 and V4, two of the largest visual areas outside the primary visual cortex in primates. V2 receives a strong direct input from V1, and depends on the functional integrity of V1 for its visual responsiveness. We will therefore develop a two-stage model, in which responses are constructed from a suitable combination of V1 afferents, with the design of each stage following a common canonical form. This model is designed to account for the visual response properties of neurons as economically as possible, allowing it to be fit to data recorded from single neurons. The model will also be able to generate population representations that can predict perceptual capabilities. V4, in turn, receives the bulk of its direct input from V2. We will measure V4 responses with the goal of building a similar model of the way it transforms input from V2. Some neurons in V4 respond selectively to images of objects and shapes while others seem to be more sensitive to local image statistics. The motivation for the structure of the V2 model, and our confidence in its success, comes from the convergence of three pieces of previous work: (1) we have developed, fit, and validated a similar two-stage model for neuronal responses in area MT, an extrastriate area which also receives primary afferent drive from area V1; (2) we have preliminary evidence for a key model element, which is to represent the operation of V2 neurons as derivatives over the space of its inputs, and (3) we have shown that models of this structure can account for our previous discovery that many V2 cells respond more vigorously to naturalistic texture stimuli than to matched noise. We will complement the modeling by analyzing the local structure of natural images and the psychophysical performance of human observers in the space that the model is designed to capture. We are not yet ready to build a principled model of how V4 combines inputs from V2. We believe that V4's functional circuitry will be similar to that of V2, but in advance of the model we will build for V2 we lack a sufficiently precise account of V4's inputs. But we have evidence from previous studies of V4 and from human neuroimaging data that a key component of V4's response is its selectivity for complex forms, so we will make measurements of V4 responses along a key image continuum between natural form and image statistics, and will also measure the role of contextual signals in establishing V4's selectivity. The outcome of this work will be a new understanding of the functions of V2 and V4, which plays a pivotal role in the elaboration of visual information in the cerebral cortex.